Question
Question: If sin (a + b) sin (a – b) = sin g (2 sinb + sing), 0 \<a, b, g\<p, then the family of lines sinax +...
If sin (a + b) sin (a – b) = sin g (2 sinb + sing), 0 <a, b, g<p, then the family of lines sinax + sin by + sing = 0 passes through
A
(–1, 1)
B
(1 , 1)
C
(1, –1)
D
(–1, –1)
Answer
(–1, 1)
Explanation
Solution
sin (a + b) sin (a – b) = sin g(2 sin b + sin g)
(2 sin b + sin g)
Ž sin2 a – sin2 b = 2 sin b sin g + sin2 g
Ž sin2 a – (sin b + sin g)2 = 0
Ž (sin a – sin b – sin g) (sin a + sin b + sin g) = 0
Since, 0 < a, b, g < p
So, sin a + sin b, sin g > 0
sin a + sin b + sin g ¹ 0
So, sin a – sin b – sin g = 0
or, (–1) sin a + 1 . sin b + sin g = 0
Hence x sin a + y sin b + sin g = 0
passes through (–1, 1).